Hello, and welcome for the second part of the course on fluidized bed encapsulation, in which I will focus on heat and mass transfer principles and the formation of the microstructure. I will subdivide after a short introduction into fluid spray particle interaction considerations, then followed by principles of heat and mass transfer in the fluid ice bed, finally coated particle/capsule and agglomerate microstructure generation, and summary conclusions. Some nomenclature again and let me start again, as usual with the S-Pro Squared scheme, because process makes structure, structure defines property. And from a food structure and functionality design perspective, we always start from the consumer side in a reverse engineering approach. The consumer is interested in preference, acceptance, need profiles to be fulfilled.
And it’s mainly preference for the controlled release of aroma flavour compounds or nutritive compounds and protection of functional components against unwanted reactions which we want to achieve by encapsulation in the fluidized bed in this specific case. We also look for powder flowability as a technofunctional property for the powder handling of major interest in this context. Structure is again pellets, agglomerates, capsules on the macro scale. Mesoscale is particles and also networks of binder molecules. And on a microscale, we have the molecules of the binders, as well as the functional component molecules. The processing is related to coating or agglomeration. Both are possible methods to encapsulate as we will see during this course talk.
Let me start with looking at the spray drops into the three phase systems which are acting in fluidized bed reactors. And the droplets, besides the particles and the gas flow, are an important phase, because they have to meet the particles in order to form a shell for coated particles or the binder parts for agglomerate formation. So accordingly, the tailoring of the drop size distribution having narrow size distributions, and also an optimised flight distance of the droplets to the surface of the particles, is of importance. The latter is certainly depending on the drying and collision conditions in the systems.
This is crucial in order to fulfil the objectives of having a controlled formation of a coating layer or a close coating layer, and also the formation of closely-packed agglomerates, which are efficient in encapsulation. For this, we have spray parameters to be considered and specific spraying nozzles– mostly preferred two-face spraying nozzles. Means air-assist nozzles with INMIX or EXMIX type of characteristics are of interest. Spraying in the fluidized bed system has to be controlled by the thermodynamic operation point which we want to keep constant. Our control parameters is outlet air temperature and outlet air relative humidity in the system. And accordingly, we have to adjust process variables and ambient variables, as shown here in this scheme.
And take into account the rate of evaporation of the coating media fluids, which is a function of the fluidization of the air– means the velocity, temperature, and humidity. And this impacts on the film formation of interest. Accordingly, the spray rate is fixed, which depends on evaporation capacity of the air, the stickiness of the coating film, and particle velocity in the coating zone.
Coating solution droplet size is adjusted relative to coated particle size, and this is also done by the atomization of the droplets at a certain flow rate, spray pressure, and spray fluid viscosity, and rheology characteristics, as well as spray fluid surface interfacial tension in order to have a well-defined drop size and coding layer or binding points formed in the product. For small particle diameter, smaller than 250 microns, we certainly have to have very small droplets in order to have even coating and agglomeration made available. In the next slide, I show you a bit about the typical mechanisms. Droplets meet the surface of particles, so small drops may also collide due to Brownian motion, as we have in the case c.
But typically, there is some collision by interception or inertia of the bit larger drops between 10 and 40 microns on the particles which typically have 100 microns to one millimetre size. The particle wetting is important– so when the droplet hits the surface. The wetting is certainly very important. So we want to have good wetting in order to form a layer. And the wetting energy, which is crucial for this, can be defined as a function of interfacial tension, the contact angle, and the surface area, which is wetted according to this equation 1.
So wetting exists when the wetting angle is smaller than 90 degrees, which has to be adapted by the choice of the liquid or components within the liquid, like emulsifiers and so forth.
When we look at the contact angle in further detail in the dynamic situation, we can see that when the drop hits the surface of a particle– here this is shown for a flat or approximately flat surface. So we can see that the advancing contact angle and the receding contact angle are different. So this is to be considered. And we certainly want to have the largest possible area wetted. And accordingly, we have to take the following aspects into prominent account. So first, the value of the dynamic contact angle always depends on the velocity of the contact line. So moving positive or negative, as shown in this figure of the slide.
So second, the advancing static contact angle is larger than the receding contact angle. And third, more than one value of the contact angles is possible for stationary contact lines. So as we can see here, we have quite a range in the static angle domain.
Some simulation results from shapes of droplets, which are hitting the surface and developing over a dimensionless time, which is defined here– tall. And we can see how it’s spreading and maybe receding again. We would certainly like to keep it in a spread state in order to cover the largest possible surface. But in general, due to interfacial tension effects, there is some receding. We can identify the governing dimensionless parameters– Reynolds, Weber, and Bond numbers– to be relevant for the consideration of this wetting process and the development of this drop shape touching the surface. Surface energy of the spreading droplet can be defined as shown in equation 2 with an equilibrium contact angle and the liquid gas interfacial area.
As well as a liquid solid interfacial area to be considered. Comparisons between numerical simulation and experimental results for the formation or the deformation of a drop and the formation of a flat layer, and the related contact angle governing this type of motion. As well as in the second diagram, the ratio of the diameter of the area, which is wetted, divided by the drop diameter. So this is also denoted as a spread diameter. So these are the two major criteria, and we can see that simulation and experiments are in quite good agreement. So this is for two different experiments with glycerin drops or glycerin water drops and water drops on different surfaces, like glass and wax surfaces.
So the number of the experiment 4 and 7 is also reflected in these two diagrams. So drop-particle adhesion– so when the drop has hit and somehow covered some part of the interface of the particles, so we have adhesion characteristics or adhesion mechanisms due to the pressure acting during the drop which is hitting the surface. Some thermal adhesion characteristics– diffusion may play a role in the penetrating of the liquid with the surface of the particle and chemical reactions. Can also be physical reactions, like maybe some partial melting and so forth, but also chemical reactions, which can be happening.
The adhesion probability is determined by the kinetics momentum of the drop hitting the surface, the characteristics of the surface in contact, and physical chemical properties like hydrophilic/hydrophobic surface characteristics. When we look for the drying part, we can enter into an overview by a diagram suggested by Molerus and Wirth, which gives us the motion of the air, which is denoted by the omega number. Here we have the velocity of the air and the particle size, which is in a dimensionless form given by the Arrhenius number. The Arrhenius number couples both, so we have the velocity and the particle size included.
In a fluidized bed system which has porosities between 0.5 and 1, which would certainly be the state of parametric conveying, we can read out the relationships between particle size and the superficial velocity of the air. The environmental particle property and gas property parameters allow us to formulate six different dimensionless groups, which are denoted here. And for the heat transfer, mainly the Nusselt number, and also the Prandtl number are of specific interest, as we will see. Let’s start with the range of large Arrhenius numbers. So in that range, 10 to the 5 to 10 to the 8. If I go back to the diagram, we can see 10 to the 5, 10 to the 8.
So we are in this upper region, where we more or less have again a straight line, which means a power law relationship in the diagram. So there is– from Molerus and Wirth, we have adapted some– we get an equation, equation 6, which gives us the maximum heat transfer coefficient, which is related to the Prandtl number in this case for the high range of Arrhenius numbers. What we have to distinguish, or what we can distinguish in this range, is whether we have purely particle convective heat transfer or purely gas convective heat transfer, which are the extremes for increasing gas velocities. We certainly approach the purely gas convective heat transfer.
Larger particles certainly also come down from the curve 1 to the curve 4, due to the higher Archimedes numbers which we have acting for the larger particles. If you go for small Archimedes number, so means laminar flow domain, we can approximate according to Molerus with this simple equation– the maximum heat transfer coefficient as given by equation 10. What is a bit more difficult is the intermediate domain in Arrhenius numbers between the 10 to the second to 10 to the 5. This is a domain where we have quite a complex description of an equation, which gives us the heat transfer coefficient.
Just to mention the l which we can see coupled with the heat transfer coefficient, is always the characteristic length scale, ll for the laminar flow, as we had it before. Let me just go back. For the high Archimedes numbers, we can see here the lt is the characteristic length scale for the turbulent flow. As we can also get from the diagram shown on this slide here is that numerical simulation or model-based calculations and experiments are in quite good agreement according to this complex type of equation number 11. The drawing of the pellets has to follow. Or let’s say, the heat transfer is meant to dry the liquid drops which are deposited on the surface of the particles.
And accordingly, we have to go for mass transfer. So a mass flux of liquid to surface of a pellet during the drying can be written like shown here. The drying force is this partial pressure difference between the partial pressure of solvent in the air and the partial pressure of the solvent over the surface of the pellet. So the letter, we get from the Antoine equation, as given in the equation 14. In the second drawing stage, we have a reduction of the equilibrium vapour pressure. And this reduction is modelled with an exponential function here, showing the reduction in equation 15.
Based on these assumptions of this exponential decay, we can get some Sherwood number for the mass transfer, as shown in equation 19. And finally, the solvent mass fraction can be related to the film thickness, according to a simple mass balance equation, as given in equation 20.
The variables, which we have in the equation 19, is the Schmidt number, and also this dimensionless transfer coefficient.
With the energy equation for the pellets, where we can consider convection and evaporation as given in equation 20, and a coupling with mass and energy conservation of the fluid phase completes the modelling approach for fluidized bed heating and drawing of the pellets. And the models are already quite advanced, and there is quite a number of semi-empirical model modifications also given and adjusted to different systems treated in fluidized beds– coating and drying.
A bit of an alternative approach for mass transfer in the fluidized beds– a bit more empirically adjusted by an alternative to the approach from Gunn, which was already published in 1976, is the one which Fabrizio Scala has suggested based on experimental data which were excellently fitted with a slightly modification of an equation of the so-called Frossling type approximation where we can see the relation between the Sherwood number– means the dimensionless mass transfer, the porosity of the fluidized bed, as well as the Reynolds and the Schmidt number.
When we go into some spray film coating model, we can simply derive such from a mass balance. So this model can also be related then to the heat and mass transfer equations shown before. And the coupling gives us then the film thickness, which can be derived or which can be calculated. This is shown for smaller and larger particles. In the first diagram, we see here on the bottom of these slides the mean residence time in the spray zone for smaller and larger particles. So there is mixtures of 1,749 microns and 2,665 micron particles. And we can see the different residence times. So we have the larger– let’s say the fraction of the large particles.
So the more we have shift of the residence times to higher well use, which means higher probabilities or higher coating load for the spray droplets hitting the particles. When we look at the relative rate of increase of the coating thickness between the large and the small ones, we can see this higher probability for the large ones to get loaded with a binder liquid. As soon as we have the liquid droplets deposited or placed on the surface of the pellets of the particles, we have to decide on whether we want to go for coding or for agglomeration. So this is mainly decided by the amount of binder, and also the kinetics of the drying.
So adhesion increases with concentration, viscosity, surface tension, and coating solution. And of the coating solution and with the drying, because we enter through a stickiness or sticky type of domain. The more important the adhesion is the more likely the process of agglomeration will take place. And this can be influenced by the composition of the coating solution and the probability of particle contacts as a consequence of the dynamic situation in the fluidized bed. There is an approach which was suggested by Ennis, which is defining Stokes numbers– the viscous Stokes number and a kind of a critical Stokes number.
And when the viscous Stokes number is smaller, than the critical one– so the collision of particles will be successful to get into an agglomerated state. And if the reverse case is valid, the granules will grow by coating and not by coalescence with others. So this is a clear distinction between coating and agglomeration. Both can be of interest for immobilising or entrapping some functional material, but the more closed type of shell by coated particles is preferable if you want to have controlled release conditions adjusted. One example for a bit more complex combination of spray dried particles, which can be multiphase, and something can already be encapsulated. And then in the fluidized bed, agglomerating and maybe in addition, coating the agglomerate.
So this would be a coupling of agglomeration and coating. And so this is in a publication from Turchiuli and co-workers in 2011, and we can see what’s on in the fluidized bed process– controlling the temperature, the outlets, gas temperature, and the added mass of spraying material– spraying liquid. So we can see phase one where we have the heating up. And then in the second phase, where we have the agglomeration of the particles. And finally, the coating of the agglomerates form before.
With this I would like to summarise. For optimal encapsulation, we have to take into account a narrow size distribution of the spray drops and the spray fluids characteristics like viscosity, interfacial tension, heat capacity, and also the evaporation behaviour under the heating drying conditions. The spray fluid particle surface interactions– so the wetting capability and maybe some partial chemical or physical interaction of the spray drops with the interface. And the mean flight distance and residence time under acting thermal conditions of relevance, because whether we get a more sticky type of surface or already a dried one depends certainly on the drying conditions during the flight time of the liquid drop before it hits the interface.
For the proper consideration of local heat transfer, we can use some simulations certainly to get into some details. But it is recommended to take the particle convection and fluid gas convection contributions in the related Archimedes numbers domains into account. So we have seen that the modelling is quite different, whether we are in laminar or low Arrhenius number domains, or whether we go high up. Mass transfer models are still of more approximate nature. So far there is not much proper experimental results, but still we have some good advancement in models for the Sherwood number as a function of the Reynolds number already derived, which are waiting for getting improved in the future.
And last but not least, encapsulate structure adjustment in fluidized bed processing is still rather difficult and needs also empirical adjustment, because the interplay of the fluid, of the spray, with the particles and the fluidized bed complex dynamic conditions is something which still needs some empirical adjustment. There is a very interesting area of artificial intelligence adaptation to these type of processes, which is also very encouragingly ongoing. With this, I would like to thank you for your attention.